13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The…

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Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: In a flat geographic region, the course of two rivers can be represented approximately by the…

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Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: The slope of the tangent line to the parabola y 2x + 3x +6 at the point (1, 11) is: The equation of…

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Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

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Q: What is the maximum vertical distance between the line y =x +2and the parabola y =x2 for     -1 ≤ x…

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Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

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Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

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Q: On a separate piece of paper, sketch the graph of the parabola y = x² + 9. On the same graph, plot…

A: Sketch the figure.

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: Find equations of both the tangent lines to the ellipse x2 +4y2 =36that pass through the point (12,…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – axis…

A: Solution

Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

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Q: Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the…

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Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: Find the point on the parabola y= -X-+4 whose tangent line is parallel with y= 3x-5,

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Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: What is the smallest possible area of the triangle that is cutoff by the first quadrant and whose…

A: Given that the triangle that is cut off by the first quadrant and whose hypotenuse is tangent tothe…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−6x2 and the…

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Q: There is a line through the origin that divides the region bounded by the parabola y=7x-(2(x)^2) and…

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Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

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Q: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: A parabola is the set of all points in the plane that areequidistant from a fixed point called the…

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Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: Find the orthogonal trajectories of the family of parabola described by the equation (x+2} = cy.…

A: Explanation of the answer is as follows

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find